Compacted bentonite is foreseen as buffer material for high-level radioactive waste in deep geological repositories because it provides hydraulic isolation, chemical stability, and radionuclide sorption. A wide range of laboratory tests were performed within the framework of FEBEX (Full-scale Engineered Barrier EXperiment) project to characterize buffer properties and develop numerical models for FEBEX bentonite. Here we present inverse single and dual-continuum multicomponent reactive transport models of a long-term permeation test performed on a 2.5 cm long sample of FEBEX bentonite. Initial saline bentonite porewater was flushed with 5.5 pore volumes of fresh granitic water. Water flux and chemical composition of effluent waters were monitored during almost 4 years. The model accounts for solute advection and diffusion and geochemical reactions such as aqueous complexation, acid-base, cation exchange, protonation/deprotonation by surface complexation and dissolution/precipitation of calcite, chalcedony and gypsum. All of these processes are assumed at local equilibrium. Similar to previous studies of bentonite porewater chemistry on batch systems which attest the relevance of protonation/deprotonation on buffering pH, our results confirm that protonation/deprotonation is a key process in maintaining a stable pH under dynamic transport conditions. Breakthrough curves of reactive species are more sensitive to initial porewater concentration than to effective diffusion coefficient. Optimum estimates of initial porewater chemistry of saturated compacted FEBEX bentonite are obtained by solving the inverse problem of multicomponent reactive transport. While the single-continuum model reproduces the trends of measured data for most chemical species, it fails to match properly the long tails of most breakthrough curves. Such limitation is overcome by resorting to a dual-continuum reactive transport model.